Vujčić graduated from the University of Zagreb Faculty of Economics in 1988, where he also received his doctorate in 1996 with a thesis titled Ponuda rada žena i njen utjecaj na tržište rada:primjer Hrvatske (English: Labor supply of women and its impact on the labor market: the case of Croatia).
He succeeded Željko Rohatinski in July 2012. He started his professional career in 1989 as an assistant at Faculty of Economics in Zagreb. In 1996 he was named the head of research department of Croatian National Bank.
Later in 1997 he became a lecturer at Faculty of Economics in Zagreb and in 2003 an associate Professor.
Since 2000 he holds the position of Vice Governor of the Croatian National Bank, and in 2012 he reaches the position of Governor.
